On conciseness of words in profinite groups

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• 作者：Eloisa Detomi^a ; ^{detomi@math.unipd.it" class="auth_mail" title="E-mail the corresponding author} ; Marta Morigi^b ; ^{marta.morigi@unibo.it" class="auth_mail" title="E-mail the corresponding author} ; Pavel Shumyatsky^c ; ^{pavel@unb.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20E18 ; 20F12 ; 20F14
• 刊名：Journal of Pure and Applied Algebra
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：220
• 期：8
• 页码：3010-3015
• 全文大小：272 K

文摘

Let w be a group word. It is conjectured that if w has only countably many values in a profinite group G  , then the verbal subgroup w(G)$w(G)$ is finite. In the present paper we confirm the conjecture in the cases where w   is a multilinear commutator word, or the word x²$x^2$, or the word [x²,y]$[x^2,y]$.